Determine the angle between the lines whose equation are
`2x-y+3=0 and x+y-2=0`.

Answer

To determine the angle between the lines given by the equations \(2x - y + 3 = 0\) and \(x + y - 2 = 0\), we will follow these steps:

### Step 1: Find the slopes of the lines
First, we need to rewrite both equations in the slope-intercept form \(y = mx + c\), where \(m\) is the slope.

1. For the first equation \(2x - y + 3 = 0\):
\[ -y = -2x - 3 \implies y = 2x + 3 \]
Thus, the slope \(m_1 = 2\).

2. For the second equation \(x + y - 2 = 0\):
\[ y = -x + 2 \]
Thus, the slope \(m_2 = -1\).

### Step 2: Use the formula for the angle between two lines
The angle \(\theta\) between two lines can be calculated using the formula:
\[ \tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right| \]

### Step 3: Substitute the slopes into the formula
Substituting the values of \(m_1\) and \(m_2\):
\[ \tan \theta = \left| \frac{2 - (-1)}{1 + 2 \cdot (-1)} \right| \]
This simplifies to:
\[ \tan \theta = \left| \frac{2 + 1}{1 - 2} \right| = \left| \frac{3}{-1} \right| = 3 \]

### Step 4: Find the angle \(\theta\)
Now, we can find \(\theta\) using the inverse tangent function:
\[ \theta = \tan^{-1}(3) \]

### Conclusion
Thus, the angle between the two lines is:
\[ \theta = \tan^{-1}(3) \]